I think they mean that what happens when a neutron decays is well understood. One of the neutron's down quarks change to an up quark, facilitated by a virtual W boson with negative charge. The W boson is very unstable and immediately decays into an electron and an electron anti-neutrino, both of which are ejected leaving behind the former neutrino which is now a proton because of that quark change.

When that happens is less understood, hence the discrepancies you mentioned.

The same QCD theory that's used to model the proton models the neutron. Theoretically, our understanding of both is on the same footing.

The comment I replied to talked about "new physics". That's a term that's used in physics to describe physics beyond the Standard Model. Better experimental data about neutron internals could certainly help constrain the neutron lifetime, but that would be likely to be experimental constraints on existing physics, not new physics in the sense that the term is normally used.